IBM Journal of Research and Development
An algebraic approach to curves and surfaces on the sphere and on other quadrics
Selected papers of the international symposium on Free-form curves and free-form surfaces
The conformal map z→z2 of the hodograph plane
Computer Aided Geometric Design
Rational curves and surfaces with rational offsets
Computer Aided Geometric Design
Hermite interpolation by Pythagorean hodograph quintics
Mathematics of Computation
The elastic bending energy of Pythagorean-hodograph curves
Computer Aided Geometric Design
Minkowski pythagorean hodographs
Computer Aided Geometric Design
Construction and shape analysis of PH Hermite interpolants
Computer Aided Geometric Design
Hermite interpolation by pythagorean hodograph curves of degree seven
Mathematics of Computation
Minkowski Roots of Complex Sets
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
C1 Hermite interpolation using MPH quartic
Computer Aided Geometric Design
Clifford algebra, Lorentzian geometry, and rational parametrization of canal surfaces
Computer Aided Geometric Design
A control polygon scheme for design of planar C2 PH quintic spline curves
Computer Aided Geometric Design
Computer Aided Geometric Design
Topological criterion for selection of quintic Pythagorean-hodograph Hermite interpolants
Computer Aided Geometric Design
C1 Hermite interpolation with PH curves by boundary data modification
Journal of Computational and Applied Mathematics
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We prove the Weierstrass-type approximation theorem that states every C^1 curve in the 2-dimensional or 3-dimensional Euclidean space or in the 3-dimensional Minkowski space can be uniformly approximated by Pythagorean hodograph curves in the corresponding space. This abundance of PH curves is another theoretical confirmation of the usefulness and the versatility of the PH curves. We also address some algorithmic aspects of proposed PH approximation schemes and their convergence rates.